On the Complete Analogy of Complex Analysis and Real Analysis in the Field of Vectors V₂
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On the basis of the isomorphic algebraic structures of the field of complex numbers ℂ and the 2-dimensional Euclidean field of vectors V₂, in terms of identical geometric products of elements, in this paper vector integral identities have been derived for scalar and vector fields in V₂, which are vector analogues of the well-known integral identities of complex analysis. In doing so, special attention is given to the vector analogue in V₂ of Cauchy's calculus of residues.